Arabic is a Semitic language (sometimes called Afro-Asiatic). This group of languages is spread over North Africa and the Mideast. The only living languages to which Arabic has substantial relations are Hebrew and Aramaic (spoken by the Neo-Assyrians). Arabic has very little in common with most European languages, which explains why many people find it hard to learn. Arabic is the official and/or the mother tongue of over 220,000,000 people (thus called Arabs). Over 1,000,000,000 people know some Arabic for use in the practice of Islam.
Arabic (like other Semitic languages) has it's roots in proto-Semitic, a language probably spoken in Arabia first. From this proto-language arose many local dialects that differentiated and later became independent languages (much the same way as Indo-European languages emerged). Modern Arabic as we know it is descended from a language known as Northerm Arabic. In specific a dialect known as Nabataean spoken in the Levant (espectially the Nabataea valley in Lebanon). This dialect then spread to the south to western Arabia, where it developed and waited for the rise of Islam to spread. To this moment Nabataean is still thought of as a weird nomadic Arabic dialect and poetry is still written in this dialect in Lebanon and Saudi Arabia (the poets are a bit short on audience though, no one seems to understand anything they say). In western Arabia classical Northern Arabic as we know it developed. Poems written in this language as far back as 100 BC or so are still taught in high schools in Egypt today (to the pain and consternation of millions of pupils). Northern Arabic is the closest living Semitic language to proto-Semitic.
Arabic has a very wicked property that makes it even harder
to grasp. This property is called diglossia. Diglossia is a phenomenon
in which two forms of one language exist and are used side by side at the
same time. One variety is a higher, more formal one. The other is less
formal and mostly oral. This is distinct from local dialects because local
dialects do not involve people using two substantially different forms
simultaneously. Most languages exhibit some form of multiglossia, but the
starkest examples are: Arabic, Greek, Swiss German, and Haitian Creole.
Greece has recently abandoned diglossia when it switched all written, official
documents to the lower variety (Dimotiki).
Arabic has the following forms:
Written or High variety. Known as Fusha (the s and the h are independent,
pronounce fos haa). There is some confusion about this form. Classical
Arabic is sometimes used in reference to written Arabic and sometime Modern
Standard Arabic or MSA is used, so is there a difference? Actually no,
MSA is just a lite version of classical Arabic with a slightly simplified
grammar and a more "human" vocabulary. Classical Arabic has elaborate vocabulary,
complex grammar and an archaic feel. The biggest difference between the
two is word order in classical it is entirely verb-subject-object (VSO),
in MSA it can be VSO or SVO.
The second form of the language is the spoken form, sometimes inaccurately
called local dialect. Spoken forms are usually simpler and more adaptive
than the written form. The spoken form (Ammiyah, or derjeh) varies substantially
from region to region. If someone aims to "learn" Arabic he or she would
have to learn MSA/classical plus at least one local dialect,
look here for more on this.